People find all sorts of ways to lobby President Bush. Sometimes it comes in the form of a handwritten note slipped into his palm during a bill-signing ceremony.

Sen. Thomas R. Carper (D-Del.) tried that last week when Bush signed energy legislation that will curb greenhouse gases. "Congratulations and good work," Carper recalled writing. "By the way, Joe Lieberman and John Warner have a very good global warming bill that needs your support and you ought to support it."

Bush tucked the note into his pocket and promised to read it later. Carper hoped he would find it at the end of the day when he slipped his suit off. No one knows what effect such a note might have, but it was just one more small foray in a battle for Bush's attention that has been raging for years, one in which European leaders, American governors, corporate executives, evangelical preachers and key lawmakers have pressed him to lead what they see as a bid to save the planet.

For years, Bush bristled privately at what he considered sky-is-falling alarmism by the liberal, elitist Hollywood crowd. The clatter over climate change, according to friends and advisers, seemed to him more like a political agenda than a rational response to known facts. But ever so gradually, they say, Bush's views have evolved. He has found the science increasingly persuasive and believes more needs to be done, especially after a set of secret briefings last winter. A former aide said Bush's staff even developed models for a market-based cap on greenhouse emissions.

Now Bush bristles not at the Hollywood types but at the notion that he does not care. At an end-of-the-year news conference, he spent more time answering a question on climate change than on any other inquiry, outlining his approach in detail to dispel the notion that he does not have one. "I take the issue seriously," he said, later repeating the phrase. "And we're developing a strategy that will deal with it, and an effective strategy."

The evolution has been evident over the past year. Bush cited the danger of climate change in his State of the Union address for the first time, proposed a plan to cut gasoline consumption and, by extension, greenhouse gases, and convened a conference of major world polluters to start work on an international accord to follow the Kyoto Protocol. He even invited former vice president Al Gore for a 40-minute talk about global warming.

Many environmentalists dismiss this as cover for a do-nothing policy. Bush still rejects the one measure that they, and even many Republican corporate leaders, consider vital to reversing warming trends -- a mandatory cap on carbon emissions. His negotiators infuriated counterparts at this month's talks in Bali by resisting such a move. And just hours after Bush signed the energy bill, the administration invalidated an effort by California and 17 other states to impose tougher tailpipe emission rules, saying it makes more sense to have a single national policy.

"There's no question the profile has changed in a pretty dramatic way," said Eileen Claussen, president of the Pew Center on Global Climate Change and a leader of a coalition of corporations and nonprofit groups called the United States Climate Action Partnership, which has been lobbying Bush. "But the policy prescriptions haven't changed at all."

The coming year offers a final test of whether Bush is willing to move beyond the policies of the past seven years and embrace more aggressive measures, including a mandatory limit on carbon emissions with pollution credits that can be bought and sold -- a system known as cap-and-trade. If presented such legislation by Sens. Lieberman (I-Conn.) and Warner (R-Va.), supporters hope, Bush might sign it.

"They are more engaged in thinking about this in a way they were not before," said Fred Krupp, president of Environmental Defense, an advocacy group, who talks with White House officials. "That leads me to think things are still fluid there. The current public position is not what it needs to be, but I don't have the sense that it's cemented into place."

Bush's attention comes at a time when he and top advisers feel better about his presidency, confident they have turned a corner after two years of political setbacks and can now focus on reformulating his legacy. Heading into his final year, Bush has turned to big, bracing challenges abroad, most notably finding Middle East peace and forging a consensus on climate change. If global warming turns out to be a defining issue of this generation, advisers said, Bush does not want to be remembered as a roadblock.

"As you draw toward the end of an eight-year term, it's human nature to try to look forward and then backward -- look into the future and then back at the past and think about how it looks," said a former Bush adviser who spoke on the condition of anonymity. "You could conclude, as this administration has, that you want to be seen ultimately as having evolved and opened some doors and maybe started a glide path to the next administration."